@ devices come to mind - Potentiometers and encoders. Potentiometers come in linear and rotary versions.
Depending on resolution and repeatability a couple of linear potentiometers might be able to do the job, only testing would reveal the true resolution and repeatability. A couple of analog inputs and a push button to tell the Arduino when to make the measurement. Easy to do if you can find a linear pot with enough length. Accuracy - probably not so good.
Encoders - would work real nice with 2 Arduinos - one for each encoder, and a common push button. Encoders rigged to some kind of X-Y slide on the fixture - fine tooth gear drive. Resolution could be quite high - depends on the counts per rev of the encoder. Higher lower counts don't affect price too much for a given size encoder. Omron has some nice, small ones that are towards the low end of the price spectrum. Would be more work, but if built carefully it would be very accurate and repeatable. Harder to program, but good accuracy and repeatability.
Another option - various instrument manufacturers make indicators and other measuring instruments with a communication connection. Interface with that to the arduino and from the arduino to a PC.